From 81c6cd075d1b35f53ce6441cf72870d9539b672c Mon Sep 17 00:00:00 2001 From: Denis Valeev Date: Thu, 16 Apr 2026 08:31:59 -0400 Subject: [PATCH] Add interactive elementary operator atlas app --- apps/elementary-operator/index.html | 469 ++++++++++++++++++++++++++++ index.html | 6 + offline-manifest.json | 24 +- 3 files changed, 491 insertions(+), 8 deletions(-) create mode 100644 apps/elementary-operator/index.html diff --git a/apps/elementary-operator/index.html b/apps/elementary-operator/index.html new file mode 100644 index 0000000..c0e0502 --- /dev/null +++ b/apps/elementary-operator/index.html @@ -0,0 +1,469 @@ + + + + + + Elementary Functions from One Operator + + + +
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All elementary functions from a single operator

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Primitive operator: eml(x, y) = ex − ln(y)

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1. Core building blocks

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From eml and 1, we recover exponential and logarithm, then arithmetic kernels.

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E(x) = eml(x, 1),  L(x) = ln(x),  S(a, b) = eml(ln(a), eb)

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A(a, b) = a + b,  G(a, b) = a − b,  M(x, y) = xy,  D(x, y) = x/y

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Use the explorer to inspect one construct at a time and see domain restrictions.

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2. Arithmetic explorer over ℝ / ℂ

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+ exp / log +

E(x) = eml(x, 1); L(x) = eml(1, eml(eml(1, x), 1))

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Valid on ℝ with x > 0 for L(x).

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+ Domain: ℝ + Shortcut: ← / → to change operation +
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3. Branch constants & trig hooks

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In ℂ we fix a branch of Log. Principal branch gives i = eiπ/2 and π = −i Log(−1).

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sin(x) = (eix − e−ix) / 2i,  cos(x) = (eix + e−ix) / 2

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Different branches can flip signs or shift by odd multiples of π.

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+ Similarity Lab + Embedding Explorer + Value Formatter +
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Labs & tools

Cosine Similarity Lab +
  • + + + Elementary Operator Atlas + +
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